Samsung Galaxy S3 does not appear on Windows computer or Mac?

I'm trying to unlock a Samsung Galaxy S3 Gt-i9305 on EE running Android 4.3. I know how to unlock the phone however, when I connect the phone to my computer it does not appear at all. Usually, Android phones have a notification saying the phone is connected as a media device or something but it doesn't appear.

- Installing new drivers (however I don't know if they were the correct drivers I tried several though)
- Installing Kies and updating to the latest version on both Mac and Windows
- Putting my phone in download mode to download drivers (no drivers downloaded)
- Restarting the phone and taking out the sim

Is there anything else I can possibly do? Is it a hardware problem? I don't have USB debugging on either. Thank you for your help.

I'm trying to unlock the S3 from EE. I haven't bought an unlock code, I want to do it for free. There is no password on the phone, I've still unlocked the phone when it's plugged in though. Yes I've tried many USB ports and 3 different cables which all work with my S4 not my S3. I guess if my S4 works on both Windows 10 and Yosemite then the S3 should too. I don't have the original EE sim with me it's someone else's so yes I'm using a different sim in the phone. I tried without the sim and got the same result.

Have you reset the device, or do you not want to do that? Do you need to save some data / media? **I am not familiar with unlocking via pc, only with codes** through a great guy on eBay UK who I see has not traded for a few months. (Used him 3 or 4 times, needs the IMEI)

I don't know how you acquired it, but you can check in Settings - General - About Device - Status and see if it's official on the bottom. There are apps that can check if it's genuine but I don't think you can use it currently?

If it is factory reset (you can do this in Recovery mode with the phone off, via the buttons) and there is no screen lock, that is - Lock Screen is set to Swipe or None it should normally connect.